AI agents increasingly select and pay service providers without human review. In emerging permissionless markets, however, adversaries can create inexpensive identities and fabricate feedback to inflate provider reputation, making reputation-based payment authorization vulnerable to Sybil attacks and exposing clients to unbounded financial loss. This paper presents AgentValve, a protocol for Sybil-resilient payment authorization in permissionless AI markets. AgentValve builds on a trust network that represents reputation as finite capacity in a directed graph and authorizes payments through trust paths with sufficient available capacity. A smart contract atomically reserves the capacity supporting each admitted payment, bounding honest agents' payment exposure by the capacity they extend into the adversarial region, and thus creating identities or interactions entirely within that region cannot increase this bound. To limit capacity depletion by malicious senders, AgentValve combines payment-backed capacity creation with bounded route length, preventing attackers from depleting honest capacity without incurring corresponding payment costs. AgentValve further decouples off-chain route discovery from on-chain verification and introduces a witness-commit mechanism that reduces route verification to linear work while requiring only constant persistent state per admitted payment. We implement a AgentValve prototype and evaluate it using six months of Ethereum data and synthetic workloads. Experimental results show that under attacks with up to 10,000 synthetic Sybil identities and with chosen attackers, the payment exposure and capacity depletion remain bounded. Regarding practicality, the witness-commit mechanism lowers admission cost by up to 40.8% compared with baselines, and admitting common payments costs approximately \$0.04-\$0.21.

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